Simplify the expression. $ (5z^{5}-3z^{3}) - ( -7z^{5}+3z) - ( -3z^{5}-7z^{3}) $
Solution: Distribute any negative signs. $(5z^{5}-3z^{3}) + (7z^{5}-3z) + (3z^{5}+7z^{3})$ Since we are adding polynomials, we can simply remove the parentheses. $5z^{5}-3z^{3} + 7z^{5}-3z + 3z^{5}+7z^{3}$ Identify like terms. $ {5 z^5} - \color{#DF0030}{3 z^3} + {7 z^5} - {3 z} + {3 z^5} + \color{#DF0030}{7 z^3} $ Combine like terms. $ { ( 5 + 7 + 3 ) z^5} + \color{#DF0030}{ z^3} + { -3 z} $ Add the coefficients. $15z^{5}+4z^{3}-3z$